Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 9x13 inch pan.
In a large bowl, cream together the butter and sugar until light and fluffy. Beat in the eggs, one at a time, then stir in the mashed bananas.
In a separate bowl, sift together the flour, baking soda, salt, cinnamon, and nutmeg. Stir the dry ingredients into the banana mixture just until blended. Stir in the vanilla, then fold in the walnuts.
Spread the batter into the prepared pan. Bake in preheated oven for 30 to 40 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Allow to cool before frosting.
To make the frosting: In a medium bowl, combine the butter, confectioners' sugar, milk, and vanilla. Beat until smooth and creamy. Frost the cooled cake.
Interesting Facts
Banana cakes are popular in many countries around the world.
Bananas are a great source of potassium, fiber, and vitamin B6.
Banana cake is a great way to use up overripe bananas.